Just had my Catalytic Converter stolen do I need to replace it or just repair the missing section of tail pipe?

You can go without a cat...but the ECU may have to be re-mapped and you are polluting our air...the precious metals in cats are worth a lot, in case you are wondering why it would get stolen..not to use on another car

Google the emissions testing authority in your area. you can call their help line. they answer and help including directing you to the least expensive certified, verifyable help................You have to follow their directions to be compliant and able to renew license tags next time. Temporary repairs you do yourself can get you there. An automotive business has to ask, and sell the right part for what you are doing. They need to know your make, model, year etc. You can question what to do till your insurance company decides if it was covered or not.

Replace the converter cause it is the correct thing to do.

A 13 year old vehicle would not have coverage for theft of a converter. The repair of it would be up to an exhaust shop anyway. They would not do a substandard repair because the shp and the tech could face fines once you went to get tags, and then an emission test. The testing is state wide, by your address, and required until you are notified it becomes exempt. Usually 25 years, or where your address does not require it. That's why I suggested googling them an calling for specific instructions. They can send you to the help that empathizes with you, and provides a legal catalyst at reduced cost. ooooh scaaarrry!

That is, unless the vehicle had specific comprehensive coverage.........The vehicle could also be parked in a building that the contents were covered by the insurance of a homeowner or renter. Then you would get your police report to reflect the circumstances. It helps if the insurance agent was aware that vehicle parks in the hypothetical structure, and covers that structure..... You may have to pay to get your transpo going, then await the findings of the adjuster.